Stadium Shape Calculator
Calculate area and perimeter of a stadium shape — a rectangle with semicircular ends.
Enter the radius and straight-section length for instant results.
Stadium Shape (Discorectangle)
A stadium shape — also called a discorectangle or oblong — is a rectangle with a semicircle attached to each of its two shorter ends. This gives a smooth, rounded shape with no corners. Think of the outline of a running track viewed from above, a typical pill shape, or a finger ring cross-section.
Defining the shape:
- a = radius of the semicircular ends (also = half the width of the rectangle)
- b = length of each straight section (the rectangular middle part only)
- Total shape width = 2a
- Total shape length = b + 2a
Formulas:
| Property | Formula |
|---|---|
| Area | A = pi * a^2 + 2 * a * b |
| Perimeter | P = 2 * pi * a + 2 * b |
| Total Length | L = b + 2a |
| Total Width | W = 2a |
Understanding the formulas:
- Area = (full circle of radius a) + (rectangle of width 2a and length b)
- Perimeter = (full circle circumference) + (two straight sections)
Worked example — running track outline (a = 40 m, b = 80 m):
- Area: pi × 1600 + 2 × 40 × 80 = 5027 + 6400 = 11,427 m^2
- Perimeter: 2pi × 40 + 2 × 80 = 251.3 + 160 = 411.3 m
- Total length: 80 + 80 = 160 m
- Total width: 80 m
Special case — perfect circle: When b = 0, the stadium degenerates into a circle of radius a. Area = pia^2, Perimeter = 2pi*a. Both formulas reduce correctly. ✓
Where this shape appears: Athletics tracks, pharmaceutical capsule outlines (in 2D plan view), rugby and American football fields, hotdog shapes, and many architectural plans use the stadium profile. The shape is also important in computational geometry as a simple bounded region for collision detection.